Preheat oven to 375°F. Place cream cheese and milk in bowl. Microwave on HIGH for 1 minute. Whisk until smooth. Separate 1 egg using egg separator; reserve egg white. Add the yolk and remaining 7 eggs, salt and black pepper to bowl; whisk to combine.
Add chopped bell pepper and onions to egg mixture. Melt butter in 10” frying pan over medium-low heat. Add egg mixture; cook, stirring occasionally, until eggs are set but still moist. Remove pan from heat.
Unroll 1 package of crescent dough; do not separate. Arrange longest side of dough across width of 12”x15” cookie sheet. Repeat with remaining package of dough. Seal perforations. On longest sides, cut dough into strips 1 ½” apart, 3” deep (there will be 6” in the center for the filling)
Arrange ham evenly over middle of dough. Spoon eggs over ham. Sprinkle with cheddar cheese. To braid, lift strips of dough across filling to meet in center, twisting each strip one turn. Continue alternating strips to form a braid. Brush lightly beaten egg white over dough using pastry brush
Bake 25-28 minutes or until deep golden brown. Cut into slices and serve.